1. Field of the Invention
The present invention relates to the field of telecommunications. More particularly, the present invention relates to a method for generating self-similar packet traffic having selected characteristics that can be used for simulating telecommunications network behavior based on the generated self-similar packet traffic.
2. Description of the Related Art
Traditional traffic models used for characterizing the behavior of a telecommunications network, such as traffic models that are based on a Poisson process, do not sufficiently model the bursty nature of broadband telecommunications. The introduction of self-similar processes for characterizing modern network packet traffic has led to various studies for modeling and generating self-similar traffic, as well as for determining the effects of traffic self-similarity and multiplexing on queuing performance and network design. One important property of self-similar traffic is that the traffic distribution decays relatively slowly (xe2x80x9cheavy-tailedxe2x80x9d, such as a Pareto distribution) as opposed to having an exponential decay (xe2x80x9clight tailedxe2x80x9d, such as a Poisson distribution). Another important property of self-similar traffic is that self-similar traffic has a correlation exhibiting a hyperbolic decay (xe2x80x9clong range dependencexe2x80x9d, or LRD) rather than an exponential decay (xe2x80x9cshort range dependence, or SRD).
It has been demonstrated that traffic having self-similarity characteristics has a considerable impact on network buffer performance. See, for example, N. Likhanov et al., Analysis of an ATM buffer with self-similar (xe2x80x9cfractalxe2x80x9d) input traffic, in Proc. IEEE INFOCOM""95, 1995, pp. 985-992; I. Norros, A storage model with self-similar input, Queueing Syst., vol. 16, pp. 387-396, 1994; A. Erramilli et al., Experimental queuing analysis with long-range dependent packet traffic, IEEE/ACM Trans. Networking, vol. 4, pp. 209-223, April 1996; and M. Parulekar et al., Tail probabilities for a multiplexer with self-similar traffic, in Proc. IEEE INFOCOM""96, 1996, pp. 1452-1455. The extent of the impact on network buffer performance may also depend on networking arrangements. See, for example, B. S. Tsybakov et al., supra; B. Ryu et al., The importance of long-range dependence of VBR video traffic in ATM traffic engineering: Myths and realities, in Proc. ACM Sigcomm""96, 1996, pp. 3-14; and M. Grossglauser et al., On the relevance of long-range dependence in network traffic, in Proc. ACM Sigcomm""96, 1996, pp. 26-30. The persistent nature of self-similar traffic has caused a somewhat extreme belief that burstiness becomes even more bursty with multiplexing over source or time, thus casting doubt on statistical multiplexing gains based on self-similar traffic streams.
One proposed model for simulating self-similar traffic is based on a superposition of a small number of Markov modulated Poisson processes (MMPP) and is disclosed by A. T. Andersen et al., A Markovian approach for modeling packet traffic with long-range dependence, IEEE J. Select. Areas Commun., vol. 16, pp. 719-732, June 1998. Another model based on Markov renewal processes (P) has been proposed by B. E. Helvik et al., Self-similar traffic and multilevel source models, in Proc. 12th Nordic Teletraffic Seminar, Espoo, Finland, 1995, pp. 285-298; and P. C. Kiessler et al., Markov renewal models for traffic exhibiting self-similar behavior, in Proc. IEEE SOUTHEASTCON""96, 1996, pp. 76-79.
Use of a superposition of a large number of heavy-tailed on-off sources governed by chaotic maps has been proposed by P. Pruthi et al., Heavy-tailed ON/OFF source behavior and self-similar traffic, in Proc. IEEE ICC""95, 1995, pp. 445-450. A model using a superposition of a large number of heavy-tailed on-off sources governed by a Pareto distribution has been proposed by N. Likhanov et al., supra; and W. Willinger et al., Self-similarity through high-variability: Statistical analysis of Ethernet LAN traffic at the source level, IEEE/ACM Trans. Networking, vol. 5, pp. 71-86, February 1997.
A model based on fractional autoregressive integrated moving average (ARIMA) processes has been proposed by W. E. Leland et al., On the self-similar nature of Ethernet traffic (extended version), IEEE/ACM Trans. Networking, vol. 2, pp. 1-15, Febuary 1994; M. W. Garrett et al., Analysis, modeling and generation of self-similar VBR video traffic,xe2x80x9d in Proc. ACM Sigcomm""94, 1994, pp. 269-280; and M. M. Krunz et al., Modeling video traffic using M/G/∞ input processes: A compromise between Markovian and LRD models, IEEE J. Select Areas Commun., vol. 16, pp. 733-748, June 1998.
Models based on fractional Brownian motion (FBM) or fractional Gaussian noise (FGN) processes has been proposed by W. E. Leland et al., supra; W. -C. Lau et al., Self-similar traffic generation: The random midpoint displacement algorithm and its properties, in Proc. IEEE ICC""95, 1995, pp. 66-472; I. Norros, supra; and A. Erramilli et al., supra.
While the models based on Markovian and the on-off source superposition approaches have the respective advantages of being analytically tractable and physically meaningful, all the proposed models mentioned above, except for the model based on FGN, have the drawback of describing self-similarity only asymptotically and only over a limited range of time scales. The model based on FGN yields exactly second-order self-similar traffic. Nevertheless, the proposed models require intensive computations for computer synthesis of self-similar traffic traces, such as used for Monte Carlo simulation of network performance under self-similar traffic patterns.
An effective model for generating self-similar traffic is based on an M/G/∞ count process. See, for example, D. R. Cox, Long-range dependence: A review, Statistics: An Appraisal, in Proc. 50th Anniv. Conf., H. A. David et al., Eds. Ames, Iowa: Iowa State Univ. Press, 1984, Iowa State Statistical Library, pp. 55-74; and D. R. Cos et al., Point Processes, London, England: Chapman and Hall, 1980, Sec. 5.6. Such a model has been suggested for generating asymptotically second-order self-similar traffic by V. Paxson et al., Wide area traffic: The Failure of Poisson modeling, IEEE/ACM Trans. Networking, vol. 3, pp. 226-244, June 1995; and by J. -F. Frigon et al., A pseudo-Bayesian Aloha algorithm with mixed priorities for wireless ATM in Proc. IEEE PIMRC""98, 1998, pp. 45-49. It should be noted, though, that the example considered by J. -F. Frigon et al. does not lead to self-similarity because the resulting autocorrelation does not behave hyperbolically. A model based on the M/G/∞ count process has also been proposed by M. M. Krunz et al., supra, that uses on a discrete-time Poisson input process.
In view of the foregoing, what is needed is a technique for conveniently generating self-similar traffic having selected characteristics that can be used for modern simulating telecommunications network behavior based on the generated self-similar packet traffic.
The present invention provides a technique for conveniently generating self-similar traffic having selected characteristics that can be used for simulating modern telecommunications network behavior based on the generated self-similar packet traffic.
The advantages of the present invention are provided by a method for mimicking streams of self-similar traffic in a telecommunications network. A continuous-time Poisson arrival process is applied to an M/G/∞ system, such that the continuous-time Poisson arrivals have a predetermined means arrival rate and a predetermined service time distribution. A stream of self-similar traffic is generated based on the count process of the arrivals formed in the M/G/∞ system, such that the self-similar traffic has a selected mean arrival rate and a selected autocorrelation function. The generated stream of self-similar traffic is applied to a portion of a telecommunications network and a behavior of the portion of the telecommunications network is then simulated based on the applied stream of self-similar traffic. According to one aspect of the present invention, the predetermined service time distribution is selected based on the selected predetermined autocorrelation function, thereby the step of generating the stream of self-similar traffic generates self-similar traffic having an exact second-order self-similarity. According to another aspect of the present invention, the predetermined service time distribution is selected based on a desired predetermined heavy-tailed distribution function, thereby the step of generating the stream of self-similar traffic generates self-similar traffic having an asymptotic second-order self-similarity.